Now, in a saucepan, mix the roux adding your chicken broth according to the directions. When well-blended, add to the large stew pot with the other ingredients. Put in salt, pepper, thyme and cayenne. Bring to a boil and simmer for 2 hours, adding more strained stock if needed for consistency. Adjust seasonings. When it has simmered for at least two hours and the flavors have begun to blend, add the de-boned chicken and sliced sausage and cook for 15 more minutes.